Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Let, the age of the first friend = x years
So, the age of the other friend = 20 – x years
Four years ago:
Age of the first friend = x – 4 years
Age of the second friend = 20 – x – 4 = 16 – x years
According to question,
(x – 4) (16 – x) = 48
⇒ 16x – x² – 64 + 4x = 48
⇒ x² – 20x + 112 = 0
For the quadratic equation x² – 20x + 112 = 0, we have a = 1, b = – 20, c = 112.
Therefore,
D = b² – 4ac = (-20)² – 4 × 1 × 112 = 400 – 448 = – 48 < 0
So, there is no real roots of this quadratic equation.
Hence, this situation is not possible.